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Background  The extent of linkage disequilibrium (LD) within a population determines the number of markers that will be required for successful association mapping and marker-assisted selection. Most studies on LD in cattle reported to date are based on microsatellite markers or small numbers of single nucleotide polymorphisms (SNPs) covering one or only a few chromosomes. This is the first comprehensive study on the extent of LD in cattle by analyzing data on 1,546 Holstein-Friesian bulls genotyped for 15,036 SNP markers covering all regions of all autosomes. Furthermore, most studies in cattle have used relatively small sample sizes and, consequently, may have had biased estimates of measures commonly used to describe LD. We examine minimum sample sizes required to estimate LD without bias and loss in accuracy. Finally, relatively little information is available on comparative LD structures including other mammalian species such as human and mouse, and we compare LD structure in cattle with public-domain data from both human and mouse.    Results  We computed three LD estimates,  D ',  Dvol  and  r  2 , for 1,566,890 syntenic SNP pairs and a sample of 365,400 non-syntenic pairs. Mean  D ' is 0.189 among syntenic SNPs, and 0.105 among non-syntenic SNPs; mean  r  2  is 0.024 among syntenic SNPs and 0.0032 among non-syntenic SNPs. All three measures of LD for syntenic pairs decline with distance; the decline is much steeper for  r  2  than for  D ' and  Dvol . The value of  D ' and  Dvol  are quite similar. Significant LD in cattle extends to 40 kb (when estimated as  r  2 ) and 8.2 Mb (when estimated as  D '). The mean values for LD at large physical distances are close to those for non-syntenic SNPs. Minor allelic frequency threshold affects the distribution and extent of LD. For unbiased and accurate estimates of LD across marker intervals spanning < 1 kb to > 50 Mb, minimum sample sizes of 400 (for  D ') and 75 (for  r  2 ) are required. The bias due to small samples sizes increases with inter-marker interval. LD in cattle is much less extensive than in a mouse population created from crossing inbred lines, and more extensive than in humans.    Conclusion  For association mapping in Holstein-Friesian cattle, for a given design, at least one SNP is required for each 40 kb, giving a total requirement of at least 75,000 SNPs for a low power whole-genome scan (median  r  2  > 0.19) and up to 300,000 markers at 10 kb intervals for a high power genome scan (median  r  2  > 0.62). For estimation of LD by  D'  and  Dvol  with sufficient precision, a sample size of at least 400 is required, whereas for  r  2  a minimum sample of 75 is adequate.

Extent of genome-wide linkage disequilibrium in Australian Holstein-Friesian cattle based on a high-density SNP panel